o/' Bessel's Astronomical Observations. 25 



The semi-differences contained in the last column are to be 

 applied to the readings obtained by the first and third verniers 

 with their signs : but to those obtained by the second and 

 fourth verniers with the contrary signs. They are well repre- 

 sented by the formula + l"-26 + 0"6764 sin [2u + 215° 66} 

 where u denotes the reading of the first vernier. The values 

 of this formula have been constantly applied to the observa- 

 tions of the sun being added together with the deviation of 

 the wires from the parallelism, the deviation of the parallel 

 from a great circle, and the change of declination in the co- 

 lumn of the journal headed, Reduction to the Meridian. The 

 numbers for the two pole-stars contained in the same column, 

 however, do not include the deviation of the horizontal wires. 



During the observations of the sun the whole instrument 

 was screened, and only two inches of the object-glass were 

 left uncovered. But, notwithstanding this, as a considerable 

 deo-ree of heat was produced in the focus, I applied, on the 

 25th of November 1820, near the place of the wires, a stop 

 made of thin brass plate, which completely protects the ring 

 containing the wires from the rays of the sun. 



The divisions of the level of the alhidade circle were deter- 

 mined by changing, in some culminations of the pole-star, the 

 alhidade at each observation ; the value of a Paris line on the 

 scale was thus found : tl ° 



1820. April 11 1-236 Therm. = — 11 '2 C 



12 1-255 .... 14-4 



14? 1-291 .... 14*25 



20 1*254- .... 8*3 



June 27 1*182 .... 19-3 



1821. May 22 1*227 .... 10-0 



Mean . . . 1-241 

 This value has been used to convert the deviation of the 

 level given at each observation into seconds. Whenever the al- 

 hidade began to show somewhat considerable deviations, I 

 put it back by the screw of the alhidade ; in the beginning 

 this has not been mentioned in the journal, but since the 11th 

 of December, 1820, I have always remarked it whenever 1 

 have touched the screw. . 



This level has the inconvenience of having the bubble in 

 our winters extended to such a length that its extremities are 

 covered, and can no longer be observed. In order to avoid the 

 adding of spirit, I have filled the lower part of the tube to 

 about' its axis with closed glass tubes, so that it takes only 

 half the quantity of spirit of wine, and consequently shows 

 only half the effects of temperature, and may now be used 

 without alteration till the year round. 



Vol. G4. No. Si 5. My 1824. D rwwf 



